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Using Trivial Mathematics to Estimate Prime Counts with Upper and Lower Bounds, and demonstrating why Littlewood's Theorem Needs Reconsidering
2021
figshare.com
Although mathematicians have not yet found the underlying pattern to readily determine where each individual prime sits in the number line, much work has focused on the prime count density. In contrast to observable results, however there exists a theorem by Littlewood which states that the prime count π(X) can exceed the Li(X). This paper uses elementary mathematics to firstly provide a formula that generates estimates for π(X) which are less than Li(X), greater than X/ln X, and which always
doi:10.6084/m9.figshare.17125640.v1
fatcat:xrcrqrelafggdknonxtftuhbha